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Simple word problem involving exponents

  1. Jan 23, 2008 #1
    A population of rabbits triples every month. Assume we start out with 100 rabbits.

    a. How many rabbits are there after 4 months

    b. How long until there are 50,000 rabbits?


    2. Relevant equations

    ... this is where I am running into the trouble... I'm really not sure how to create the equation to solve these problems...


    The only attempt I've made at a solution has been

    100 * 3 * 3 * 3 * 3 = amount of rabbits after 4 months?

    Any help here would be greatly appreciated
     
  2. jcsd
  3. Jan 23, 2008 #2
    So we know that, at time "0", we have 100 rabbits. Every month the population triples (3x).

    [tex]x(t)=100\times 3^t[/tex]

    t=0

    [tex]x(t)=100\times 3^0[/tex]
     
  4. Jan 23, 2008 #3

    HallsofIvy

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    So your questions become

    a. How many rabbits are there after 4 months
    What is (100)34?

    b. How long until there are 50,000 rabbits?
    For what t is (100)3t= 50000?

    For that last one, you will need to use a logarithm. What is log(3t)?
     
  5. Jan 23, 2008 #4
    Ahh.. thank you! I had been staring at that problem for way too long without getting anywhere.. now I'm finally unstuck :)
     
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